Analysis of anticipation driving effect in traffic lattice hydrodynamic model with on-ramp

A new traffic lattice hydrodynamic model with on-ramp is proposed with consideration of driver’s anticipation effect according to transportation cyber physical systems. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region on the phase diagram will be enlarged by considering driver’s anticipation effect but shrunk with the consideration of on-ramp effect. In order to depict traffic jamming transition, the modified Korteweg-de Vries (mKdV) equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density wave can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results, and all the results confirm that both driver’s anticipation effect and on-ramp effect affect the traffic stability of the main road importantly.